# Fingerprint Dive into the research topics where Aleksandr Vasilievich Shapovalov is active. These topic labels come from the works of this person. Together they form a unique fingerprint.

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### Physics & Astronomy

#### General

operators

nonlinearity

principal components analysis

pulses

formalism

dissipation

Riemann manifold

propagation

Hamilton-Jacobi equation

preprocessing

strokes

Minkowski space

profiles

fractals

interactions

Yang-Mills fields

curves

wave packets

allowances

simulation

hyperbolic systems

decomposition

intervals

thermal instability

#### Physics

Dirac equation

Klein-Gordon equation

solitary waves

wave equations

perturbation

absorption spectra

equations of motion

momentum

laser beams

coefficients

nanoparticles

#### Mathematical and Computer Sciences

symmetry

algebra

nonlinear equations

differential equations

approximation

Cauchy problem

polar coordinates

partial differential equations

linear equations

automorphisms

#### Engineering

electromagnetic fields

#### Aeronautics

trajectories

#### Chemistry and Materials

air

gas mixtures

#### Aerospace Sciences

laser spectroscopy

### Mathematics

Gross-Pitaevskii Equation

Symmetry

Semiclassical Approximation

Laser Spectroscopy

Absorption Spectra

Nonlocal Equations

Gas Mixture

Evolution Operator

Nonlinearity

Principal Component Analysis

Operator

Exact Solution

Berry Phase

Cauchy Problem

Canonical Correlation Analysis

Trajectory

Solitons

Nonlinear Fokker-Planck Equations

Linear equation

Asymptotic Solution

Nonlinear Equations

Approximation

Solitary Waves

Fokker-Planck Equation

Small Parameter

Localized Structures

Analogy

Q-deformation

Linear differential equation

Integro-differential Equation

Hamiltonian Dynamics

Formation Control

Term

Intertwining Operators

Data Preprocessing

Kolmogorov Equation

Absorption Spectroscopy

Biological Tissue

Dimensional Reduction

Reaction-diffusion Model

Laser Radiation

Curve

Model

Green's function

Kink

Hamiltonian Systems

Population Model

Pattern Formation

Stroke

Hopf Algebra